Brush the cooking grates clean. Lightly brush the bread slices on both sides with oil and grill them over direct medium heat, with the lid closed, until lightly toasted, about 1 minute, turning once. Remove from the grill. Place the patties, foil side up, on the cooking grates and carefully peel off the foil. Grill over direct medium heat, with the lid closed, for about 5 minutes. Turn the patties over and spread each one with about 1 tablespoon of the ketchup mixture. Continue grilling, with the lid closed, until the meat is firm and fully cooked but still moist, 4 to 5 minutes more. Remove from the grill.
Brush the cooking grates clean. Lightly brush the bread slices on both sides with oil and grill them over direct medium heat, with the lid closed, until lightly toasted, about 1 minute, turning once. Remove from the grill. Place the patties, foil side up, on the cooking grates and carefully peel off the foil. Grill over direct medium heat, with the lid closed, for about 5 minutes. Turn the patties over and spread each one with about 1 tablespoon of the ketchup mixture. Continue grilling, with the lid closed, until cooked to 165°F, 4 to 5 minutes more. Remove from the grill.
Brush the cooking grates clean. Lightly brush the bread slices on both sides with oil and grill them over medium heat, with the lid closed, until lightly toasted, about 1 minute, turning once. Remove from the grill. Place the patties, foil side up, on the cooking grates and carefully peel off the foil. Grill over medium heat, with the lid closed, for about 5 minutes. Turn the patties over and spread each one with about 1 tablespoon of the ketchup mixture. Continue grilling, with the lid closed, until cooked to 165°F, 4 to 5 minutes more. Remove from the grill.
